Aerodynamic Shape Optimization using Adjoint Method

Abstract

Numerical shape optimization will play a strategic role for future aircraft design. It offers the possibility of designing or improving aircraft components with respect to a pre-specified figure of merit subject to geometrical and physical constraints. However, the extremely high computational expense of straightforward methodologies currently in use prohibits the application of numerical optimization for industry relevant problems. Optimization methods based on the calculation of the derivatives of the cost function with respect to the design variables suffer from the high computational costs if many design variables are used. Optimization results obtained with this brute force methodologies will be presented and their numerical costs will be discussed. However, these gradients can be efficiently obtained by solution of the continuous adjoint flow equations. DLR is actively developing and validating hand-coded adjoint solvers based upon the work of A. Jameson. The talk will outline the potential of the adjoint method for aerodynamic design optimization and will give a review of the work which has been done at DLR in this field. The continuous adjoint Euler equations will be derived for the optimization of drag reduction by constant lift, and their numerical treatment within DLR's solver FLOWer will be explained. The test case for the validation of the 'FLOWer Adjoint' code will be the staggered, transonic RAE2822 airfoil, as a quasi-2D test case. This test case allows a direct comparison with the results obtained by the flo87s code of Jameson, which is available at DLR. Finally the implementation of 'FLOWer Adjoint' within DLR's optimization system will be presented and preliminary optimization examples with this adjoint method will be shown.